Algebraic Properties of BRST Coupled Doublets

TL;DR

This paper provides an algebraic analysis of the cohomology dependence on doublets in nilpotent differentials, including BRST and Slavnov-Taylor operators, without assuming decoupled doublets or relying on power-counting.

Contribution

It characterizes the cohomology dependence on doublets for coupled and decoupled cases without power-counting assumptions, extending previous algebraic frameworks.

Findings

Cohomology dependence on doublets is characterized algebraically.

Results apply to both coupled and decoupled doublets.

No reliance on power-counting arguments.

Abstract

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operator for the doublets commutes with s (decoupled doublets) and discuss the general case where the counting operator does not commute with s (coupled doublets). The results are purely algebraic and do not rely on power-counting arguments.